Ultra-parabolic H-measures and compensated compactness
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 1, p. 47-62

We present a generalization of compensated compactness theory to the case of variable and generally discontinuous coefficients, both in the quadratic form and in the linear, up to the second order, constraints. The main tool is the localization properties for ultra-parabolic H-measures corresponding to weakly convergent sequences.

Nous présentons ici une généralisation de la théorie de la « compacité par compensation ». Le cas d'une forme quadratique et de contraintes différentielles avec coefficients variables, éventuellement discontinus en espace, est considéré. Ces contraintes différentielles peuvent être d'ordre un, mais aussi d'ordre deux. Notre outil principal est le principe de localisation pour les H-mesures ultra-paraboliques associées à des suites de fonctions faiblement convergentes.

DOI : https://doi.org/10.1016/j.anihpc.2010.10.002
Classification:  35A27,  35K55,  46G10,  42B15,  42B30
Keywords: Ultra-parabolic H-measures, Localization principles, Compensated compactness, Measure valued functions, Semi-linear parabolic equations
@article{AIHPC_2011__28_1_47_0,
     author = {Panov, E.Yu.},
     title = {Ultra-parabolic H-measures and compensated compactness},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {1},
     year = {2011},
     pages = {47-62},
     doi = {10.1016/j.anihpc.2010.10.002},
     zbl = {1211.35013},
     mrnumber = {2765509},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_1_47_0}
}
Panov, E.Yu. Ultra-parabolic H-measures and compensated compactness. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 1, pp. 47-62. doi : 10.1016/j.anihpc.2010.10.002. http://www.numdam.org/item/AIHPC_2011__28_1_47_0/

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